$K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 7x + 6$ and $ KL = 2x + 31$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {7x + 6} = {2x + 31}$ Solve for $x$ $ 5x = 25$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 7({5}) + 6$ $ KL = 2({5}) + 31$ $ JK = 35 + 6$ $ KL = 10 + 31$ $ JK = 41$ $ KL = 41$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {41} + {41}$ $ JL = 82$